Abstract
The problems of finding confidence limits for the difference between two gamma means and the difference between two upper percentiles based on samples with multiple detection limits are considered. Simple methods for constructing confidence intervals and upper tolerance limits are developed based on cube root transformation and fiducial inferences. The performances of the proposed methods are evaluated by Monte Carlo simulations and are compared with parametric bootstrap and the method of variance estimates recovery. Computational results indicate that the proposed methods provide more satisfactory results even for small samples with high proportion of nondetects. The approaches are illustrated with some practical datasets.
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Acknowledgements
The authors are grateful to two reviewers whose valuable comments and suggestions enhanced the first version of the paper. This work was supported by National Natural Science Foundation of China (12101346 and 11871294), Shandong Provincial Natural Science Foundation, China (ZR2021QA053 and ZR2021QA044), and Science and Technology Support Plan for Youth Innovation of Colleges in Shandong Province (DC2000000891).
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Wang, X., Li, X., Zhang, L. et al. Fiducial inference on gamma distributions: two-sample problems with multiple detection limits. Environ Ecol Stat 29, 453–475 (2022). https://doi.org/10.1007/s10651-022-00528-5
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DOI: https://doi.org/10.1007/s10651-022-00528-5